Math 241 F1H

Midterm Exam 1 Information and Study Guide

General Information

• Exam date, time, and location: The exam will be given during the regular class time, Wednesday, 2/15/2012, 2:00 - 2:50, in the usual room, 143 Henry Administration Building.
• Open House/office hours: Sundays, beginning at around 3:15 pm, and Tuesdays/Thursdays, beginning at around 5:15 pm, in 159 Altgeld. I am also generally available after class (just get a hold of me at the end of the hour). I'm happy to answer questions by email (ajh@illinois.edu), but keep in mind that email is best suited for quick, nontechnical questions (e.g., do we have to know XYZ?); for technical questions that require a lengthy explanation it's better to ask in person.
• Exam rules: No calculators, closed books/notes, no formula sheets, and, of course, no cheating. The problems in the exam will be such that a calculator is not needed and would not be of any help.
• Missed Exam policy. If you miss the exam with a valid excuse (e.g., illness), the exam will be counted as "excused". (See the Course Information Sheet for an explanation of an "excused" exam score.) The absence must be documented by an "absence letter" from the Dean's Office at 300 Student Services Building, 610 East John St., phone 333-0050.
• Grading. The exam will be worth approximately 100 points. See the Course Information Sheet for the complete grading policy. After the exam has been graded and the scores entered into the grading system, you can view your scores via this link.

Exam Content

Exam syllabus and checklist: Click on this link for a detailed syllabus and a section-by-section checklist of topics, concepts, formulas and techniques that you should be familiar with.

The exam will cover the material through Section 14.3, including the additional topics covered in class (n-dimensional spaces, Cauchy-Schwarz and Triangle inequalities), except for the following:

• Quadratic surfaces (Section 12.6)
• Formal definition of limits and continuity of vector functions and of functions of several variables (part of Section 13.1 and Section 14.2)
• Direction angles (p. 781 bottom - p. 782 middle)
• Formula for triple cross product a x (b x c) (Property 6 in the box on p. 790)
• Formula (11), p. 834, for curvature of a plane curve
• Formula (4), p. 841, for motion of projectiles
• Kepler's Laws (p. 845 - 846)

Concept Check and True/False questions: Below are the relevant questions from the "Concept Check" and "True/False Quiz" sections in the Stewart text. Working through these questions is an excellent way to prepare for the exam and help detect any gaps you have in your mastery of the concepts and techniques. Keep in mind, however, that these questions do not cover every topic, so you should not rely on these questions alone. To be fully prepared for the exam, you should still go through the entire material, section by section, review your class notes, and review/redo the homework problems.

• Chapter 12, p. 812-813: Concept Check: All questions except 18, 19.
  True/False Quiz: All questions except 13.
• Chapter 13, p. 849-850: Concept check: All questions except 6(d), and 9 (Kepler's Law).
  True/False Quiz: All questions except 7, 11.

Note on Calculus I/II skills. You should know all the basic differentiation and integration techniques (product rule, chain rule, integration by substitution, etc.), but you need not know some of the more obscure and specialized integration tricks (e.g., for integrating powers of secant). You should know the basic trig identities (in particular, sin² + cos² = 1), and you should know the values of trig functions (cos, sin, etc.) at angles 0, Pi/6, Pi/3, Pi/4, Pi/3, Pi/2, etc. (Remember that calculators are not allowed in exams.) Questions asking about angles will either involve only one of those standard angles, or will ask you leave the answer in terms of inverse trig functions (e.g., sin^-13/8).

Note on computations: All exam problems will be carefully chosen so that, if approached correctly, any numerical computations required will be straightforward and should not take more than a minute or two. If you find yourself entangled in tedious calculations, you are almost certainly on the wrong track. In that case, it is best to move on to the next problem and return to the problem at the end if you have time left. Don't try to solve problems by brute force. For homework problems, when you have an unlimited amount of time, a brute force approach may eventually lead to a correct solution, but in an exam situation such an approach would be counterproductive as it would take time away from the other problems. This is illustrated by Problem 13 from HW 2: the statements (a)--(c) can all be proved very easily using properties of derivatives; by contrast, trying to prove these statements by componentwise evaluation leads to very messy calculations. While some students managed to prove the results in this way and received full credit in the homework, such an approach would not be a practical option in an exam.

Sample exams. Click on this link for sample exams. These exams should give you an idea of the length and difficulty level of the exam, and the types of problems that you may encounter. (Note that there may be small differences in material covered in each midterm due to differences in the syllabus, text, and the timing of the exams.)

Advice for exam day

• Read the problems carefully. This is one of the most important tips. All the information you need to solve a problem is given in the statement of the problem. If a problem doesn't seem to make sense at first glance, read it again; perhaps you missed a key piece of information given in the problem. Try to categorize the problem by topic or section in the book, and think of the concepts and problems associated with this topic; chances are that a similar problem has come up before.
• Use common sense. The problems on the exam have been carefully selected to be appropriate for an hour exam. They are intended to test your knowledge of the material and techniques and should be neither ridiculously easy, nor excessively hard or lengthy. There are no trick questions. If your solution seems too easy to be true, it probably is, and you may have mis-interpreted the problem or missed a key assumption. Similarly, if you get entangled in a lengthy computation, you are likely on the wrong path.
• Show all work, use correct notation, write legibly, and circle/box your final answer. An answer alone, without justification, will not earn credit. Be sure use correct notation; in particular, distinguish vectors from scalars by arrow notation, use explicit clearly visible dots for dot products, etc.
• If you make a mistake, cross out all of your incorrect work. We will take points off for incorrect work that is not crossed out, even if the correct answer is given elsewhere on the page. (This is a common sense grading policy. Without such a policy, someone who isn't sure which of two possible methods is the correct one, would be assured to get credit simply by working out both methods, thereby covering all bases!)
• Budget your time wisely. You have 50 minutes for the entire exam. This is more than adequate if you are well prepared and have the relevant concepts and formulas at your finger tips, but you need to work efficiently and not waste time. There will be a total of 6 - 8 problems on the exam, which works out to an average of 6 - 8 minutes per problem. Take a look at the sample exams above to get a sense of the length of a typical exam; all of these were written as 50 minute exams, though the best students usually finished in 30 minutes or less.
  If you find yourself working 10 minutes or more on a single problem, chances are that you are on the wrong track, and you will be better off moving on to the next problem. You can always get back to this problem if you have time left over at the end.
• Note on calculations. The calculations required for the exam are very minimal. Many of the problems require no calculations whatsoever, and for those that do the computations are simple and can easily be performed in your head (recall that calculators are not allowed in this course). You can generally leave answers in "raw" form, such as 3/Sqrt{14}, 3 Pi/5, etc. (though you should evaluate standard trig values, e.g., sin(Pi/4)). If you get entangled in a lengthy calculation, you are likely on the wrong track, perhaps missing an easier approach. (With some problems, there may be two possible approaches, one quick and easy, and the other lengthy and messy; it is your job to know and use the more efficient approach.) If you spend more than a few minutes total time on calculations for a single problem, you are wasting your time.

Last modified: Sun 12 Feb 2012 02:26:04 PM CST A.J. Hildebrand